Your Abacus Teacher

Your step-by-step interactive assistant for mastering abacus bead by bead.

Operators:
Select Formula
Breaking down the logic...

Touch to Move

Tap or click any bead directly on the rods to move it up or down.

Place Value Decomposition
Language:

Abacus Formulas & Mental Math Calculation Guide

Mastering mental arithmetic on the soroban abacus relies on complementary bead movement rules: Small Friend Formulas (base 5 complements) and Big Friend Formulas (base 10 complements).

Small Friend Addition (+5 Complements)

Used when lower beads (value 1 each) are full and the upper bead (value 5) is available:

  • +4 = +5 − 1   (Add 5, remove 1)
  • +3 = +5 − 2   (Add 5, remove 2)
  • +2 = +5 − 3   (Add 5, remove 3)
  • +1 = +5 − 4   (Add 5, remove 4)

Big Friend Addition (+10 Complements)

Used when a column reaches capacity (value 9) and needs to carry over to the next tens column:

  • +9 = +10 − 1   (Add 10, remove 1)
  • +8 = +10 − 2   (Add 10, remove 2)
  • +7 = +10 − 3   (Add 10, remove 3)
  • +6 = +10 − 4   (Add 10, remove 4)

How to Practice with the Simulator

  1. Guided Mode: Enter any math expression (e.g. 4 + 3) to watch step-by-step bead movements and voice explanations.
  2. Manual Mode: Click or tap beads directly on the digital abacus to set numbers, perform mental calculations, and check live values.
Switch to Manual Mode to Operate the Abacus